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Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine‐Gordon Equations
Author(s) -
Beals Richard,
Tenenblat Keti
Publication year - 1988
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1988783227
Subject(s) - inverse scattering transform , inverse scattering problem , mathematics , mathematical analysis , sine , transformation (genetics) , nonlinear system , scattering , generalized inverse , inverse , inverse problem , physics , geometry , biochemistry , chemistry , optics , quantum mechanics , gene
The generalized wave equations and generalized sine‐Gordon equations are known to be associated to linear spectral problems. In this paper we show that the geometric Backlund transformation for the nonlinear equations corresponds to changing the discrete part of the scattering data for the linear problems.